Matching a chelator (DOTA) with ions for radio-pharmaceutical applications using DFT study.

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MATCHING A CHELATOR (DOTA) WITH IONS FOR RADIO- PHARMACEUTICAL APPLICATIONS USING DFT STUDY

EBENEZER KWABENA FRIMPONG

215068623

Submitted in fulfillment of the requirements for the degree of Masters in Pharmaceutical Sciences in the School of Health Science, University of KwaZulu-Natal

Supervisors Dr Bahareh Honarparvar

Dr Adam A. Skelton

December 2016

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MATCHING A CHELATOR (DOTA) WITH IONS FOR RADIO- PHARMACEUTICAL APPLICATIONS USING DFT STUDY

EBENEZER KWABENA FRIMPONG

215068623 2016

A dissertation submitted to the School of Health Sciences, College of Health Science, University of KwaZulu-Natal, Westville, for the degree of Master of Pharmaceutical Sciences.

This is a dissertation by manuscript with an overall introduction and final summary.

This is to certify that the content of this dissertation is the original research work of Mr. Ebenezer Kwabena Frimpong, supervised by:

Supervisor: Signed: ---Name: Dr B. Hornarparvar Date: ………

Co-Supervisor: Signed: ---Name: Dr A.A. Skelton Date: ………..

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DECLARATION

I, Mr. Ebenezer Kwabena Frimpong, declare as follows:

1. That the work defined in this dissertation has not been submitted to UKZN or any other tertiary institution for purposes of obtaining an academic qualification, whether by myself or any other party.

2. That my contribution to the project was as follows:

 The research reported in this dissertation, except where otherwise indicated, is my original work

 This dissertation does not contain other person’s data, pictures, graphs or other information, unless specifically acknowledged as being sourced from other persons.

3. This dissertation does not comprise other person’s writing, unless specifically acknowledged as being sourced from other researchers. Where other written sources have been quoted, then:

 Their words have been re-written but the general information attributed to them has been referenced.

 Where their exact words have been used, then their writing has been placed in italics, inside quotation marks and duly referenced.

Signed:

EK. Frimpong

Student Number 215068623 Date: 12/12/2016

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DEDICATION

This work is dedicated to my parents Mr and Mrs Frimpong who gave me the peradventure to get education.

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ACKNOWLEDGEMENTS

I wish to express my indebtedness gratitude to the following persons for their indispensable support and unwavering support during the study:

 Dr. Bahareh Hornarparvar for excellent and distinguished supervision of my work, her extensive knowledge of the subject, publication experience and intellectual leadership.

 Dr. Adam A. Skelton, (Co-supervisor), for accepting my flaws and mentoring me to be good scientist.

 My close friends Emmanuel Apau, Isaac Ofori, Maxwell Opoku, Daniel Amoako, Fatima Ifeachioma, Bilal, Zaynab, Muhammed, Hamit, Monsurat Lawal, Emiliene Tata and Patrick Appiah Kubi for their continued unrestricted support.

 Last but not least my siblings and family for their prayers and support.

 I Thank God my Father for making it possible for me to go this far. Thank-you Jesus Christ. I am humbled by your grace and I trust you will guide me through the remaining journey.

 I would like to acknowledge the financial support from the College of Health Sciences.

Any omissions and deficiencies that may be recognized in this piece of work remain the sole responsibility of the researcher.

E.K Frimpong Durban 2016

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LIST OF PUBLICATIONS

Publications in peer review journals included in this thesis

Ebenezer Frimpong, Adam A. Skelton, Bahareh Honarparvar, DFT Study of the Interactions between DOTA Chelator and Competitive Alkali Metal Ions, Tetrahedron. Under review.

Contributions:

Ebenezer Frimpong ran the project, carried out all calculations and wrote the paper as the main author.

B. Honarparvar and A. A. Skelton – Supervisors

Ebenezer Frimpong, Adam A. Skelton, Bahareh Honarparvar. Non-covalent interactions between DOTA as a bifunctional chelator with radiometal ions for radiolabeling: A DFT study, under submission.

Contributions:

Ebenezer Frimpong ran the project, carried out all calculations and wrote the paper as the main author.

B. Honarparvar and A. A. Skelton – Supervisors

OTHER RESEARCH OUTPUT

Conference: International AIDS society official volunteer scientific poster presentation section, 21^st International AIDS Conference (18-22 July 2016), Durban, SA

Workshop: Certificate of participation Center for High performance computing (CHPC) in conjunction with University of Kwa Zulu Natal (UKZN) AMBER workshop with renowned software developers Ross Walker (University of California, San Diego) and Adrian Roitberg (University of Florida) January,2016, Westville Campus, Durban

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LIST OF FIGURES

Chapter 1

Figure 1: Commonly used chelators. A: Molecular structure of DOTA; B: Molecular structure of NOTA, C:

Molecular structure of TETA; E: Molecular structure of CB-TE2A; F: Molecular structure of CB-DO2A.

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Figure 2: Molecular structures of A: Cu2 (DOTA).5H2O; B: [Ga (HDOTA).5.5H2O]; C: 3(Na [Sc

(DOTA)]).18H2O; D: In (III) complex of P-aminoanilide. 3

Figure 3: Radionuclides used in medicine. 5

Figure 4: Principle of Positron Emission Tomography (PET). 6 Chapter 2

Figure 1: The structure of 1, 4, 7, 10-tetraazacyclododecane-1, 4, 7, 10-tetraacetic

acid (DOTA). 17

Figure 2: Optimized structures of DOTA―ion complexes: DOTA―Na⁺, DOTA―Li⁺, DOTA―K⁺

and DOTA―Rb⁺. 21

Figure 3: A presentation of the charge transfer for DOTA―ion complexes shown in NBO analysis

using second perturbation theory 28

Chapter 3

Figure 1: The structure of 1, 4, 7, 10-tetraazacyclododecane-1, 4, 7, 10-tetraacetic

acid (DOTA). 36

Figure 2: a: The optimized complexes from DOTA―Sc³⁺ crystal structure; b: denotes geometry optimized complexes from DOTA―Ga³⁺ crystal output file; c: The optimized structures from DOTA―In³⁺ complex. Carbonyl oxygen in close contact with an ion (O^C). Nitrogen and carbonyl oxygen in close contact with an ion (N). Nitrogen and carbonyl oxygen not in close contact with an

ion (N*). 40

Figure 3: Conformation of the DOTA―ion complexes: DOTA―Cu²⁺, DOTA―Ga³⁺, DOTA―In³⁺

and DOTA―Sc³⁺. In this diagram, the intermolecular distances between DOTA’s heteroatoms

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interacting with the selected radiometal ions are marked by dotted lines. 'A': DOTA―Cu²⁺ and DOTA―Ga³⁺ have 4N and 2O in close proximity with ions. 'B': DOTA―In³⁺ and DOTA―Sc³⁺have 4N and 4O atoms within (≤ 2.5 Å) range. Carbonyl oxygen (O^C) are in close contact with an ion.

Nitrogen and carbonyl oxygen atoms are in close contact with an ion (N). Nitrogen is in close contact with an ion but carbonyl oxygen is not in close proximity (N^*). 41

Figure 4. a: DOTA―Cu²⁺ and DOTA―Ga³⁺ theoretically optimized structures, b: DOTA―Cu²⁺

experimental x-ray structure, c: DOTA―Ga³⁺ experimental x-ray structure, d: DOTA―In³⁺ and DOTA―Sc³⁺ theoretically optimized structures, e: DOTA―Sc³⁺ experimental x-ray structure, f:

DOTA―In³⁺ experimental x-ray structure, Oeq: Equatorial Oxygen; Oax: axial Oxygen; Neq:

equatorial nitrogen; Nax: axial nitrogen. 47

Figure 5: A presentation of the charge transfer for DOTA―ion complexes shown in NBO analysis

using second perturbation theory. 52

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LIST OF TABLES

Chapter 1

Table 1: Experimental data obtained for DOTA complexed with radiometal ions 4

Chapter 2

Table 1: Relative energies for different DOTA― ion complexes in kcal/mol. 21 Table 2: The interaction, relaxation and counterpoise corrected energies of the DOTA―alkali metal ion complexes in vacuum and solvent obtained by B3LY P/6-311G+(2d,2p) and Def2-TPVZ basis set for Rb⁺. 22 Table 3: Thermodynamic properties of the alkali metal complexed with DOTA obtained by B3LYP/6-

311G+(2d,2p) and Def2-TPVZ basis set for Rb⁺. 24

Table 4: The average interatomic distances (Å) between ions and N, O atoms of DOTA (≤3.5 Å) obtained by the DFT/B3LYP method with 6-311 G+ (2d, 2p) as basis set and Def2-TPVZ for Rb⁺. 25

Table 5: Natural atomic charges (NAC) of classified atoms obtained by B3LYP/6-311+G(2d,2p) and

Rb⁺(Def2-TPVZ). 26

Table 6: The second-order perturbation energies, 𝐸⁽²⁾ (kcal/mol), corresponding to significant donor → acceptor charge transfers within DOTA―alkali metal complexes obtained by B3LYP/6-311+G(d,p) level of

theory and Def2-TPVZ basis set for Rb⁺. 27

Table 7: The energy eigenvalues of the frontier molecular orbitals (EHOMO, ELUMO) for the selected alkali metal ions and DOTA―alkali metal ion complexes obtained by B3LYP/6-311G+(2d,2p) and Def2-TPVZ for Rb⁺.

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Table 8: DFT-based quantities for DOTA chelator complexed with alkali metals (Li⁺, Na⁺, K⁺ and Rb⁺) obtained by B3LYP/6-311G+(2d,2p) and Def2-TPVZ for Rb⁺. 30

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xii Chapter 3

Table 1: The relative energies (kcal/mol) for the selected DOTA―radiometal ion complexes. 40

Table 2: The interaction, relaxation and BSSE energies of the DOTA―radiometal ion complexes in vacuum and solvent obtained by B3LYP/6-311G+(2d,2p) and DGDPVZ basis set for ions. 42

Table 3: The enthalpies, Gibbs free energies, entropy and its individual contributions (Translational, rotational, and vibrational) of the radiometal ions complexed with DOTA obtained by B3LYP/6-311G+(2d,2p) and

DGDPVZ basis sets. 44

Table 4: The theoretical and experimental Gibbs free energies (ΔGtheo and ΔGexp) with their corresponding

binding constants (logKtheo and logKexp). 45

Table 5: The average short-range interatomic distances between radiometal ions and DOTA’s heteroatoms in the optimized structures obtained by the B3LYP density functional with 6-311G+ (2d, 2p)/DGDPVZ basis sets.

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Table 6: Average theoretical short-range interatomic distances (Å) between ions and N, O atoms of DOTA (≤

2.5 Å) obtained by the B3LYP method with 6-311G+ (2d, 2p) and DGDPVZ basis sets for ions. Parentheses

show experimental results. 47

Table 7: Natural atomic charges of classified hetero-atoms of DOTA obtained by B3LYP/6-311+G(2d,2p)

and DGDPVZ basis set for ions. 49

Table 8: Second order pertubation theory analysis of Fock matrix in NBO basis of selected calculated values in each DOTA―ion complex obtained by B3LYP/6-311G+(2d,2p) and DGDPVZ basis sets for ions. 51 Table 9: The energy eigenvalues of the frontier molecular orbitals (EHOMO, ELUMO) for the selected metal ions and DOTA―radiometal ion complexes obtained by B3LYP/6-311G+(2d,2p) and DGDPVZ

basis sets for ions. 53

Table 10: DFT-based quantities for DOTA chelator complexed with radiometals obtained by B3LYP/6-

311G+(2d,2p) and DGDPVZ basis sets for ions. 54

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APPENDICES CHAPTER 2

Table S1. Absolute translational entropies (cal mol^-1 K^-1) for free ions and DOTA―ion complexes obtained by B3LYP/6-311G+(2d,2p) and Def2-TPVZ basis set for Rb⁺. 63 Table S2. The average interatomic distances (Å) between ions and N, O atoms of DOTA (≤3.5 Å), within 3- arm conformations of DOTA―alkali metal complexes, obtained by the DFT/B3LYP method with 6-311 G+

(2d, 2p) basis set and Def2-TPVZ for Rb⁺. 63

Table S3. Natural atomic charges of ions, within 3-arm conformations of DOTA―alkali metal complexes, obtained by B3LYP/6-311+G(2d,2p) and Rb⁺(Def2-TPVZ). 64

CHAPTER 3

Table S1. Absolute translational entropies (cal mol^-1 K^-1) for free ions and DOTA―ion complexes obtained by B3LYP/6-311G+(2d,2p) and DGDPVZ basis set for ions. 65 Table S2. Natural atomic charges of ions, within 3-arm conformations of DOTA―radiometal complexes, obtained by B3LYP/6-311+G(2d,2p) and DGDPVZ basis set for ions. 65

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LIST OF ABBREVIATIONS AND ACRONYMS

AO Atomic orbitals

B3LYP Becke,3-Parameter,Lee-Yang-Parr

BFC Bifunctional chelator

CBDO2A 4,10-bis(carboxy-methyl)-1,4,7,10-

tetraazabicyclo[5.5.2]tetradecane CBTE2A ,4,11-bis(carboxymethyl)-1,4,8,11-te

ttraazabicyclo[6.6.2]hexadecane

CPCM Conductor-like Polarizable Continuum Model

CHX-A''-DTPA CHX-A”-diethylenepentaacetic acid

Def2-TZVPD Def2-triple zeta valence polarized with one diffused function

DFT Density Functional Theory

DGDZVP Density Gauss Double Zeta Valence Polarized basis set DOTA 1, 4, 7, 10-tetraazacyclododecane-1, 4, 7, 10-tetraacetic acid

EA Electron Affinity

ECP Effective Core Potential

GUI Graphical User Interface

HOMO I Highest Occupied Molecular Orbital

HPLC I High Performance Liquid Chromatography

IP I Ionization Potential

LANL2DZ Los Alamos natural laboratory 2-double -Z

LP Lone Pair

LUMO Lowest Unoccupied Molecular Orbital

MEP Minimum Energy Path

MRI Magnetic Resonance Imaging

NAC Natural Atomic Charge

NBO Natural Bond Orbital

NOTA 1 1,4,7-triazacyclononane-triacetic acid

PES Potential Energy Surface

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PET Positron Emission Tomography

QM Quantum Mechanics

SCRF Self-consistent reaction field

SMD Solvation Model

SPECT Single Photon Emission Computed Tomography

TETA 1,4,8,11-tetraazacyclotetradecane-N,N',N'',N'''-tetraacetic acid

TLC Thin Layer Chromatography

ωB97XD Dispersion density functional

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ABSTRACT

Organometallic chelators can be potentially used for radiometal-based pharmaceuticals. The bifunctional chelator, which is covalently bound to a lead compound, forms a stable chelator―ion complex to deliver an isotope, as a labelling agent, towards a specific in vivo target. The quest to find the optimal match between chelators and radiometal ions is of interest in the field of radio pharmaceuticals. A loss of radiometal ion from a chelator without reaching to its specific target organ in vivo could be disastrous to the body. The present project is focused on the complexation of 1, 4, 7, 10-tetraazacyclododecane-1, 4, and 7, 10-tetraacetic acid (DOTA) with alkali metals and radiometal ions. Herein, we investigated DOTA―alkali metal ions complexes with density functional theory using B3LYP and ωB97XD functionals and the 6-311+G(2d,2p) basis set for Li⁺, Na⁺and K⁺ and Def2-TZVPD for Rb⁺. Conformational possibilities, starting from x-ray crystal structures and considering a different number of arms (2, 3 and 4) interacting with the ions were explored. Interaction and relaxation energies, thermochemical parameters, HOMO/LUMO energies, ΔEHOMO-LUMO and chemical hardness indicate the decrease in the stability of DOTA―ions down the alkali metal series.

Natural bond orbital analysis reveals charge transfer between DOTA and alkali metals. Regarding radiometal ions, the geometries for the various complexes were consistent with experimentally reported binding constants. NBO analysis indicates charge transfer from the chelator to the radio metals resulting in reduced positive atomic charge values for all the ions. DOTA―Ga³⁺, DOTA―In³⁺ and DOTA―Sc³⁺

complexes recorded higher ΔELUMO-HOMO energies and chemical hardness values. The DOTA―Cu²⁺

complex was the least stable among the selected complexes. This study serves as a guide to researchers in the field of organometallic chelators, particularly; radio-pharmaceuticals in finding the efficient optimal match between chelators and different metal ions.

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CHAPTER 1 INTRODUCTION

1.1 Chelation and chelator types: Acyclic and macrocyclic

The importance of the chelation process in science is enormous and cannot be overlooked. Research has revealed that the technological applications of chelators and the chelation process have been widely embraced in our industries. Chelator binds a radiometal ion to release an isotope to a specific target organ in vivo [1]. Diethylenetriaminopentaacetic acid (DTPA) was synthesized by Frost for the first time[2]. Complexation of DTPA and its derivatives with radio metals (¹¹¹In, ²¹³Bi, ^86/90Y,

177Lu, 99mTc and ^67/68Ga) are used in the field of medicine. DTPA derivatives are preferred over DOTA regarding radiomettalation of monoclonal antibodies. CHX-A''-DTPA is used for radio immunotherapy [3-5]. For the labelling of biomolecules with 99mTc acyclic chelators are mostly applied. The labeling reactions were performed using required temperatures, tetra amine based ligands with 99mTc gave good results against all other chelators. They formed a good complex showing high kinetic inertness [6-11].

DOTA, NOTA, TETA and CB-TE2A with Ga³⁺, In³⁺, Y³⁺, Lu³⁺ and Cu²⁺ ions used for the radiometallation of peptides improve, the pharmacokinetics of radiopharmaceuticals[12]. CB-TE2A derivatives have been developed lately to solve the high blood concentration of DOTA and TETA complexes with copper [13-16]. NOTA is a hexa-dentate N3O3 chelator. NOTA complexes with

67/68Ga and ^64/67Cu are more stable [17, 18].

Thermodynamic stability of their radiometal complexes make the macrocyclic chelators a preferred choice than acyclic chelators. These chelators are more kinetically inert to dissociation. Macrocyclic chelator experienced reduction in entropic loss during its co-ordination. Significant decrease in entropic loss associated with acyclic chelators make it thermodynamically unfavorable [19-24].

1.2 DOTA

Stetter and Frank reported synthesis of DOTA in 1976[25]. DOTA (1, 4, 7, 10-tetra acetic acid) is a twelve-membered tetraaza macro cycle (Figure 1) which contains four pendant carboxylate arms connected, to cyclen amines. It is a bifunctional chelator (BFC). One terminus co-ordinates a radio metal ion and the other holds, a bioactive molecule during its operations. DOTA complexes show

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high kinetic stability. In medical resonance imaging (MRI), DOTA-ligands are employed as contrasting agents for the treatment of cancer. DOTA is the potential chelator used for the preparation of lanthanide radiopharmaceuticals for therapeutic purposes [26] and form stable complexes with these ions: ^67/68Ga, ¹¹¹In, ^86/90Y and ^64/67Cu [27-34].

Figure 1. Commonly used chelators. A: Molecular structure of DOTA; B: Molecular structure of NOTA, C:

Molecular structure of TETA; E: Molecular structure of CB-TE2A; F: Molecular structure of CB-DO2A.

1.3 Significance of our study in radio-pharmaceutical applications

The loss of radiometal ions from a chelator without reaching its target organ in vivo, in the presence of these biological competitive ions (Na⁺ and K⁺) is one of the main setbacks in radiopharmaceuticals.

Finding the optimal match between a chelator and radiometal ions is of great importance to researchers. It is notable that alkali metal ions found in body have the capacity to compete with radiometals coordinated with DOTA for therapeutic and diagnosis of diseases which could affect, radiolabeling efficiency of the chelator. Quantum mechanical calculations were performed to study the interactions between DOTA and alkali metal ions to compare their stabilities in aqueous and vacuum and that of chelator―radiometal ions complexes.

1.4 Co-ordination chemistry of DOTA with radiometal ions based on crystallographic data Distorted octahedral structure (coordination number 6) has been reported for DOTA and copper complex (Figure 2A) [35]. Hexa-coordinated structure (distorted octahedral) between DOTA and

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Ga (III) was reported in 2006 (Figure 2B) [36]. Bombieri et al reported an octa-coordinated square prismatic geometry exhibited by Single crystal of [Sc(DOTA)]^- (Figure 2C)[37]. Indium forms a robust complex with DOTA (Table 1). There is no reported crystallographic data available for In (III) and DOTA complex other than its amide-armed derivatives In (III) of P-amino amide (Figure 2D) which shows twisted (~28˚) square anti-prismatic geometry (Figure 2D)[38, 39].

Figure 2. Molecular structures of A: Cu2 (DOTA).5H2O; B: [Ga (HDOTA).5.5H2O]; C: 3(Na [Sc (DOTA)]).18H2O; D: In (III) complex of P-aminoanilide.

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Table 1. Experimental data obtained for DOTA complexed with radiometal ions[1].

DOTA, 1,4,7,10- tetraazacyclododecane1,4,7,10- tetraacetic acid, maximum CN = 8,

donor set N4O4

Radiometal ions

Radiolabeling conditions

LogKML Geometry

64Cu²⁺

25–90 1C, 30–60 min, pH 5.5–6.5

22.2, 22.7

Distorted octahedron

67/68Ga³⁺

37–90 1C, 10–30 min, pH 4.0–5.5

21.3 (pM 15.2, 18.5)

Distorted octahedron

44/47Sc³⁺

95 1C, 20–30 min, pH 4.0

27.0 (pM 26.5) Square antiprism

111In³⁺

37–100 1C, 15–60 min, pH 4.0–6.

23.9 (pM 17.8–

18.8)

**Square antiprism

**No known x-ray structure available for this complex.

1.5 Radiopharmaceuticals

Radiopharmaceuticals are drugs that consist of two components: a radionuclide that transmits the mechanism of action through its decay and a targeting, biomolecule or organic ligand that reveals the localization of the radio pharmaceutical and their route of administration mainly through intravenous injection.

1.5.1 Therapeutic

They release ionizing (radiation) to affected targets in our bodies. Availability of therapeutic isotopes and finding its exact location in diseased tissues is the main challenge in the field of radiotherapy [40].

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Figure 3. Radionuclides in medicine. Different colors refer to the radiations they emmit as indicated on top of the figure.

1.5.2 Diagnostic radiopharmaceuticals

A diagnostic radiopharmaceutical employ gamma-emitting isotope for single photon emission computed tomography (SPECT) or a positron-emitting isotope for positron emission tomography (PET). Low concentrations (10⁻⁶ – 10⁻⁸ M) preferred for its operation. It is significant to point out that it should not have any pharmacological effects [41-47].

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Figure 4. Principle of Positron Emission Tomography (PET) [48].

1.6 Radiometal-based radiopharmaceutical design

Functional chelators (BFCs) are used to design radiometal-based radiopharmaceuticals. They have reactive functional groups that aid its conjugation to targeting vectors such as: nucleotides, antibodies, peptides and nanoparticles. Aqueous coordination chemistry properties of each radiometal ion should be given the needed attention to harness the potential of its isotopes for medical applications. Besides, there are several key design options considered and applied across the globe [49].

1.7 Important factors for finding the optimal match between a chelator and radiometal ion 1.7.1 Thermodynamics and kinetics

Potentiometric and spectrophotometric titrations are used to determine thermodynamic stability of metal-chelate complex. pM value (-log [M]free]) gives more important biological information than KML. It is a condition dependent value obtained from log KML. Both (pM and log KML) provide a number which helps the direction of metal co-ordination reactions takes under certain conditions.

Unfortunately, they do not supply kinetic information such as, off-rates dissociation [1],[50, 51]. Acid dissociation experiments are important to determine the stability of metal-complex to acidic conditions. Experiments are performed at a constant PH of 2.0[21],[52, 53].

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7 1.7.2 In vitro and in vivo stability

In vivo translation involves metal exchange competitions with mixtures that are biologically relevant.

HPLC and TLC are employed to assess the quantity a radio metal trans chelates from a chelator to serum protein or enzymes. It is significant to point out that, in vivo gives more relevant information regarding, radiopharmaceutical stability. The higher the stability of a radiometal―chelate complex, the more a complex is removed rapidly from the kidneys and digestive systems [54-59].

1.8 Computational background

Computer models are useful regarding complexation phenomena inspection. In the absence of extensive experimental data they offer fast measurement of predictability.

1.8.1 Theoretical models

They are used in describing systems through a particular set of approximations. Depending on approximations, algorithms are then applied to atomic orbitals to calculate energies, compute frequencies and perform geometry optimizations of molecules. Quantum and non-quantum mechanical methods (use classical physics laws, such as the equation of motion [60] are employed in computational chemistry. Quantum Mechanics (QM) methods(electronic structure theories) aims at solving Schrödinger equation (1926) to study properties of molecules [61, 62]. This model consist of the following: Semi-empirical methods (employed to study large organic molecules)[63], Ab initio methods (provide accurate qualitative results as well as, quantitative estimation) for a variety of systems[64].

1.8.2 Density functional theory

To design a more effective electronic structure method, Kohn, Sham and Hohenberg proposed, density functional models[65, 66]. Electron densities are used to compute energies, instead of wave functions.

The most popular among DFT methods is B3LYP. Correlation energies are calculated from electron densities using, exact exchange and gradient corrected density functional approximations [67-70].

1.8.3 Basis sets

Basis sets are used for the mathematical description of electron wave functions. Basis sets predict the shape of atomic orbitals (AOs) of the molecule using, a particular theoretical model[62] . The bigger the basis set, the better the computational output, since approximations of the orbitals gained by

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imposing less restriction, on the location of electrons in space. DFT (B3LYP) method will be combined with, 6-311+G(2d,2p)[71, 72], LANL2DZ[73] and DGDZVP[74, 75] for our study.

1.8.4 Geometry optimization

Separation of nuclear and electronic degrees of freedom by Born-Oppenheimer approximation gives an idea of a chemical reaction as nuclei moves on a potential energy surface (PES). Based on transformation of one chemical species to another, easiest path from one minimum to another is along the reaction path having the lowest energy known as minimum energy path (MEP). Optimization of geometries of reactants is necessary in order to predict the lowest possible minima on the potential energy surface (PES)[62, 76].

1.8.5 Solvation studies

Self-consistent reaction field (SCRF)[77]keyword is employed to calculate the effect of solvation.

This highlights the dielectric constant for the different solvents with Conductor-like Polarizable Continuum Model (CPCM)[78] and the SMD solvation model[79].

1.8.6 Computational programs

The Gauss View is a pre- and post-processor Graphical User Interface (GUI) program for Gaussian09.

All molecules will be modelled, manipulated and viewed through this suite[80, 81].

1.9 Aim of the project

The main goal of this thesis is the application of quantum chemical calculations to find the optimal match between DOTA chelator and ions particularly radiometal ions applied in the field of radiopharmaceuticals for in vivo radiolabeling. The loss of an ion from a chelator without reaching its target in vivo in the presence of competitive ions (Na⁺ and K⁺) could be disastrous to the human body.

Employing quantum mechanical calculations we will examine the stabilities of DOTA―alkali metals complexes as well as DOTA―radiometal ions complexes. It is necessary to find out which of the radiometal ions could probably serve as the optimal match for DOTA chelator to achieve in vivo radiolabeling.

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9 1.9.1 Specific objectives

A. Understanding the structure and physical properties of the chelator―radiometal ions complexes and their impact, on the overall pharmacokinetic properties of radio-pharmaceuticals.

B. Confirming aqueous co-ordination chemistry properties of radio-metal ions.

C. Examining the proposed geometry of chelator―radiometal ions complexes.

D. Comparing the stability of chelator―radiometal ions complexes as opposed to experimentally reported binding constants.

E. To propose and recommend observed chelator―radiometal ions complexes (optimal match) based on theoretical results obtained.

F. To confirm the need to carry out radio-labelling experiments involving, chelator and biologically competitive active ions based on DOTA―alkali metal ions using theoretical calculations.

1.10 Outline of this thesis Chapter 1, is the thesis introduction.

Chapter 2, focus on the interactions between DOTA and alkali metal ions to compare their stabilities in gaseous and aqueous media.

Chapter 3, investigates the interactions within DOTA―radiometal ions complexes in gaseous and aqueous media

Chapter 4, provides a summary of the dissertation.

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References

[1] Price, E. W., and Orvig, C. (2014) Matching chelators to radiometals for radiopharmaceuticals, Chemical Society Reviews 43, 260-290.

[2] Frost, A. E. (1956) Polyaminopolycarboxylic acids derived from polyethyleneamines.

[3] Milenic, D. E., Roselli, M., Mirzadeh, S., Pippin, C. G., Gansow, O. A., Colcher, D., Brechbiel, M. W., and Schlom, J. (2001) In vivo evaluation of bismuth-labeled monoclonal antibody comparing DTPA-derived bifunctional chelates, Cancer Biotherapy and Radiopharmaceuticals 16, 133-146.

[4] Roselli, M., Milenic, D. E., Brechbiel, M. W., Mirzadeh, S., Pippin, C. G., Gansow, O. A., Colcher, D., and Schlom, J. (1999) In vivo comparison of CHX-DTPA ligand isomers in athymic mice bearing carcinoma xenografts, Cancer biotherapy & radiopharmaceuticals 14, 209-220.

[5] Milenic, D. E., Garmestani, K., Chappell, L. L., Dadachova, E., Yordanov, A., Ma, D., Schlom, J., and Brechbiel, M. W. (2002) In vivo comparison of macrocyclic and acyclic ligands for radiolabeling of monoclonal antibodies with 177 Lu for radioimmunotherapeutic applications, Nuclear medicine and biology 29, 431-442.

[6] Cescato, R., Maina, T., Nock, B., Nikolopoulou, A., Charalambidis, D., Piccand, V., and Reubi, J.

C. (2008) Bombesin receptor antagonists may be preferable to agonists for tumor targeting, Journal of Nuclear Medicine 49, 318-326.

[7] Decristoforo, C., Maina, T., Nock, B., Gabriel, M., Cordopatis, P., and Moncayo, R. (2003) 99mTc- Demotate 1: first data in tumour patients—results of a pilot/phase I study, European journal of nuclear medicine and molecular imaging 30, 1211-1219.

[8] Maina, T., Nock, B., Nikolopoulou, A., Sotiriou, P., Loudos, G., Maintas, D., Cordopatis, P., and Chiotellis, E. (2002) [99mTc] Demotate, a new 99mTc-based [Tyr3] octreotate analogue for the detection of somatostatin receptor-positive tumours: synthesis and preclinical results, European journal of nuclear medicine and molecular imaging 29, 742-753.

[9] Nock, B. A., Maina, T., Béhé, M., Nikolopoulou, A., Gotthardt, M., Schmitt, J. S., Behr, T. M., and Mäcke, H. R. (2005) CCK-2/Gastrin receptor–targeted tumor imaging with 99mTc-labeled minigastrin analogs, Journal of Nuclear Medicine 46, 1727-1736.

[10] Nock, B. A., Nikolopoulou, A., Galanis, A., Cordopatis, P., Waser, B., Reubi, J.-C., and Maina, T. (2005) Potent bombesin-like peptides for GRP-receptor targeting of tumors with 99mTc: a preclinical study, Journal of medicinal chemistry 48, 100-110.

[11] Nock, B., Nikolopoulou, A., Chiotellis, E., Loudos, G., Maintas, D., Reubi, J., and Maina, T.

(2003) [99mTc] Demobesin 1, a novel potent bombesin analogue for GRP receptor-targeted tumour imaging, European journal of nuclear medicine and molecular imaging 30, 247-258.

[12] Buchmann, I., Henze, M., Engelbrecht, S., Eisenhut, M., Runz, A., Schäfer, M., Schilling, T., Haufe, S., Herrmann, T., and Haberkorn, U. (2007) Comparison of 68Ga-DOTATOC PET and 111In- DTPAOC (Octreoscan) SPECT in patients with neuroendocrine tumours, European journal of nuclear medicine and molecular imaging 34, 1617-1626.

[13] Prasanphanich, A. F., Nanda, P. K., Rold, T. L., Ma, L., Lewis, M. R., Garrison, J. C., Hoffman, T. J., Sieckman, G. L., Figueroa, S. D., and Smith, C. J. (2007) [64Cu-NOTA-8-Aoc-BBN (7-14)

(28)

11

NH2] targeting vector for positron-emission tomography imaging of gastrin-releasing peptide receptor-expressing tissues, Proceedings of the National Academy of Sciences 104, 12462-12467.

[14] Sprague, J. E., Peng, Y., Sun, X., Weisman, G. R., Wong, E. H., Achilefu, S., and Anderson, C.

J. (2004) Preparation and biological evaluation of copper-64–labeled Tyr3-octreotate using a cross- bridged macrocyclic chelator, Clinical cancer research 10, 8674-8682.

[15] Lewis, E. A., Boyle, R. W., and Archibald, S. J. (2004) Ultrastable complexes for in vivo use: a bifunctional chelator incorporating a cross-bridged macrocycle, Chem. Commun., 2212-2213.

[16] Boswell, C. A., Regino, C. A., Baidoo, K. E., Wong, K. J., Bumb, A., Xu, H., Milenic, D. E., Kelley, J. A., Lai, C. C., and Brechbiel, M. W. (2008) Synthesis of a cross-bridged cyclam derivative for peptide conjugation and 64Cu radiolabeling, Bioconjugate chemistry 19, 1476-1484.

[17] Notni, J., Pohle, K., and Wester, H.-J. (2012) Comparative gallium-68 labeling of TRAP-, NOTA- , and DOTA-peptides: practical consequences for the future of gallium-68-PET, EJNMMI research 2, 1-5.

[18] Cooper, M. S., Ma, M. T., Sunassee, K., Shaw, K. P., Williams, J. D., Paul, R. L., Donnelly, P.

S., and Blower, P. J. (2012) Comparison of 64Cu-complexing bifunctional chelators for radioimmunoconjugation: labeling efficiency, specific activity, and in vitro/in vivo stability, Bioconjugate chemistry 23, 1029-1039.

[19] Byegård, J., Skarnemark, G., and Skålberg, M. (1999) The stability of some metal EDTA, DTPA and DOTA complexes: Application as tracers in groundwater studies, Journal of radioanalytical and nuclear chemistry 241, 281-290.

[20] Stimmel, J. B., and Kull, F. C. (1998) Samarium-153 and lutetium-177 chelation properties of selected macrocyclic and acyclic ligands, Nuclear medicine and biology 25, 117-125.

[21] Stimmel, J. B., Stockstill, M. E., and Kull Jr, F. C. (1995) Yttrium-90 Chelation Properties of Tetraazatetraacetic Acid Macrocycles, Diethylenetriaminepentaacetic Acid Analogs, and a Novel Terpyridine Acyclic Chelator, Bioconjugate chemistry 6, 219-225.

[22] Camera, L., Kinuya, S., Garmestani, K., Wu, C., Brechbiel, M. W., Pai, L. H., McMurry, T. J., Gansow, O. A., Pastan, I., and Paik, C. H. (1994) Evaluation of the serum stability and in vivo biodistribution of CHX-DTPA and other ligands for yttrium labeling of monoclonal antibodies, Journal of nuclear medicine: official publication, Society of Nuclear Medicine 35, 882-889.

[23] Harrison, A., Walker, C., Parker, D., Jankowski, K., Cox, J., Craig, A., Sansom, J., Beeley, N., Boyce, R., and Chaplin, L. (1991) The in vivo release of 90 Y from cyclic and acyclic ligand-antibody conjugates, International journal of radiation applications and instrumentation. Part B. Nuclear medicine and biology 18, 469-476.

[24] Hancock, R. D. (1992) Chelate ring size and metal ion selection. The basis of selectivity for metal ions in open-chain ligands and macrocycles, Journal of chemical education 69, 615.

[25] Stetter, H., and Frank, W. (1976) Complex Formation with Tetraazacycloalkane‐N, N′, N ″, N‴‐

tetraacetic Acids as a Function of Ring Size, Angewandte Chemie International Edition in English 15, 686-686.

[26] Liu, S., and Edwards, D. S. (2001) Bifunctional chelators for therapeutic lanthanide radiopharmaceuticals, Bioconjugate chemistry 12, 7-34.

(29)

12

[27] Fani, M., Andre, J. P., and Maecke, H. R. (2008) 68Ga‐PET: a powerful generator‐based alternative to cyclotron‐based PET radiopharmaceuticals, Contrast media & molecular imaging 3, 53- 63.

[28] Aime, S., Cabella, C., Colombatto, S., Geninatti Crich, S., Gianolio, E., and Maggioni, F. (2002) Insights into the use of paramagnetic Gd (III) complexes in MR‐molecular imaging investigations, Journal of magnetic resonance imaging 16, 394-406.

[29] Caravan, P. (2006) Strategies for increasing the sensitivity of gadolinium based MRI contrast agents, Chemical Society Reviews 35, 512-523.

[30] Heppeler, A., Froidevaux, S., Eberle, A., and Maecke, H. (2000) Receptor targeting for tumor localisation and therapy with radiopeptides, Current medicinal chemistry 7, 971-994.

[31] Maecke, H. R., Hofmann, M., and Haberkorn, U. (2005) 68Ga-labeled peptides in tumor imaging, Journal of Nuclear Medicine 46, 172S-178S.

[32] Pandya, S., Yu, J., and Parker, D. (2006) Engineering emissive europium and terbium complexes for molecular imaging and sensing, Dalton Transactions, 2757-2766.

[33] Reubi, J. C., Mäcke, H. R., and Krenning, E. P. (2005) Candidates for peptide receptor radiotherapy today and in the future, Journal of Nuclear Medicine 46, 67S-75S.

[34] Tanaka, K., and Fukase, K. (2008) PET (positron emission tomography) imaging of biomolecules using metal–DOTA complexes: a new collaborative challenge by chemists, biologists, and physicians for future diagnostics and exploration of in vivo dynamics, Organic & biomolecular chemistry 6, 815- 828.

[35] Riesen, A., Zehnder, M., and Kaden, T. A. (1986) Metal complexes of macrocyclic ligands. Part XXIII. Synthesis, properties, and structures of mononuclear complexes with 12‐and 14‐membered tetraazamacrocycle‐N, N′, N ″, N‴‐tetraacetic Acids, Helvetica chimica acta 69, 2067-2073.

[36] Viola, N. A., Rarig, R. S., Ouellette, W., and Doyle, R. P. (2006) Synthesis, structure and thermal analysis of the gallium complex of 1, 4, 7, 10-tetraazacyclo-dodecane-N, N′, N ″, N‴-tetraacetic acid (DOTA), Polyhedron 25, 3457-3462.

[37] Benetollo, F., Bombieri, G., Calabi, L., Aime, S., and Botta, M. (2003) Structural variations across the lanthanide series of macrocyclic DOTA complexes: insights into the design of contrast agents for magnetic resonance imaging, Inorganic chemistry 42, 148-157.

[38] Clarke, E. T., and Martell, A. E. (1991) Potentiometric and spectrophotometric determination of the stabilities of In (III), Ga (III) and Fe (III) complexes of N, N′, N ″-tris (3, 5-dimethyl-2- hydroxybenzyl)-1, 4, 7-triazacyclononane, Inorganica chimica acta 186, 103-111.

[39] Liu, S., He, Z., Hsieh, W.-Y., and Fanwick, P. E. (2003) Synthesis, characterization, and X-ray crystal structure of In (DOTA-AA)(AA= p-aminoanilide): a model for 111In-labeled DOTA- biomolecule conjugates, Inorganic chemistry 42, 8831-8837.

[40] McEwan, A. (1997) Unsealed source therapy of painful bone metastases: an update, In Seminars in nuclear medicine, pp 165-182, Elsevier.

[41] Banerjee, S., Pillai, M. R. A., and Ramamoorthy, N. (2001) Evolution of Tc-99m in diagnostic radiopharmaceuticals, In Seminars in nuclear medicine, pp 260-277, Elsevier.

(30)

13

[42] Jain, D. (1999) Technetium-99m labeled myocardial perfusion imaging agents, In Seminars in nuclear medicine, pp 221-236, Elsevier.

[43] Jurisson, S. S., and Lydon, J. D. (1999) Potential technetium small molecule radiopharmaceuticals, Chemical reviews 99, 2205-2218.

[44] Liu, S. (2007) Ether and crown ether-containing cationic 99m Tc complexes useful as radiopharmaceuticals for heart imaging, Dalton Transactions, 1183-1193.

[45] Liu, S., and Edwards, D. S. (2002) Fundamentals of receptor-based diagnostic metalloradiopharmaceuticals, In Contrast Agents II, pp 259-278, Springer.

[46] Liu, S. (2004) The role of coordination chemistry in the development of target-specific radiopharmaceuticals, Chemical Society Reviews 33, 445-461.

[47] Reichert, D. E., Lewis, J. S., and Anderson, C. J. (1999) Metal complexes as diagnostic tools, Coordination Chemistry Reviews 184, 3-66.

[48] Wadas, T. J., Wong, E. H., Weisman, G. R., and Anderson, C. J. (2010) Coordinating radiometals of copper, gallium, indium, yttrium, and zirconium for PET and SPECT imaging of disease, Chemical reviews 110, 2858-2902.

[49] Bartholomä, M. D., Louie, A. S., Valliant, J. F., and Zubieta, J. (2010) Technetium and gallium derived radiopharmaceuticals: comparing and contrasting the chemistry of two important radiometals for the molecular imaging era, Chemical reviews 110, 2903-2920.

[50] Martell, A. E., and Smith, R. M. (1977) Other organic ligands, Vol. 3, Springer.

[51] Morfin, J.-F., and Tóth, É. (2011) Kinetics of Ga (NOTA) formation from weak Ga-citrate complexes, Inorganic chemistry 50, 10371-10378.

[52] Jonathan, P. (1991) Structure and solution stability of indium and gallium complexes of 1, 4, 7- triazacyclononanetriacetate and of yttrium complexes of 1, 4, 7, 10-tetraazacyclododecanetetraacetate and related ligands: kinetically stable complexes for use in imaging and radioimmunotherapy. X-Ray molecular structure of the indium and gallium complexes of 1, 4, 7-triazacyclononane-1, 4, 7-triacetic acid, Journal of the Chemical Society, Perkin Transactions 2, 87-99.

[53] Kubíček, V. c., Havlickova, J., Kotek, J., Tircsó, G., Hermann, P., Tóth, É., and Lukeš, I. (2010) Gallium (III) Complexes of DOTA and DOTA− Monoamide: Kinetic and Thermodynamic Studies, Inorganic chemistry 49, 10960-10969.

[54] Zeglis, B. M., and Lewis, J. S. (2011) A practical guide to the construction of radiometallated bioconjugates for positron emission tomography, Dalton Transactions 40, 6168-6195.

[55] Price, E. W., Zeglis, B. M., Cawthray, J. F., Ramogida, C. F., Ramos, N., Lewis, J. S., Adam, M.

J., and Orvig, C. (2013) H4octapa-trastuzumab: versatile acyclic chelate system for 111In and 177Lu imaging and therapy, Journal of the American Chemical Society 135, 12707-12721.

[56] Bailey, G. A., Price, E. W., Zeglis, B. M., Ferreira, C. L., Boros, E., Lacasse, M. J., Patrick, B.

O., Lewis, J. S., Adam, M. J., and Orvig, C. (2012) H2azapa: a Versatile Acyclic Multifunctional Chelator for 67Ga, 64Cu, 111In, and 177Lu, Inorganic chemistry 51, 12575-12589.

[57] Ferreira, C. L., Lamsa, E., Woods, M., Duan, Y., Fernando, P., Bensimon, C., Kordos, M., Guenther, K., Jurek, P., and Kiefer, G. E. (2010) Evaluation of bifunctional chelates for the development of gallium-based radiopharmaceuticals, Bioconjugate chemistry 21, 531-536.

(31)

14

[58] Ferreira, C. L., Yapp, D. T., Lamsa, E., Gleave, M., Bensimon, C., Jurek, P., and Kiefer, G. E.

(2008) Evaluation of novel bifunctional chelates for the development of Cu-64-based radiopharmaceuticals, Nuclear medicine and biology 35, 875-882.

[59] Li, W., Ma, D., Higginbotham, C., Hoffman, T., Ketring, A., Cutler, C. S., and Jurisson, S. (2001) Development of an in vitro model for assessing the in vivo stability of lanthanide chelates, Nuclear medicine and biology 28, 145-154.

[60] Maeda, S., Harabuchi, Y., Ono, Y., Taketsugu, T., and Morokuma, K. (2015) Intrinsic reaction coordinate: Calculation, bifurcation, and automated search, International Journal of Quantum Chemistry 115, 258-269.

[61] Hehre, W. J. (2003) A guide to molecular mechanics and quantum chemical calculations, Wavefunction Irvine, CA.

[62] Foresman, J., and Frish, E. (1996) Exploring chemistry, Gaussian Inc., Pittsburg, USA.

[63] Schrödinger, E. (1926) An undulatory theory of the mechanics of atoms and molecules, Physical Review 28, 1049.

[64] Ghosh, S. K., and Chattaraj, P. K. (2013) Concepts and Methods in Modern Theoretical Chemistry: Electronic Structure and Reactivity, CRC Press.

[65] Hohenberg, P., and Kohn, W. (1964) Inhomogeneous electron gas, Physical review 136, B864.

[66] Kohn, W., and Sham, L. J. (1965) Self-consistent equations including exchange and correlation effects, Physical Review 140, A1133.

[67] Becke, A. D. (1993) Density‐functional thermochemistry. III. The role of exact exchange, The Journal of chemical physics 98, 5648-5652.

[68] Lee, C., Yang, W., and Parr, R. G. (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Physical review B 37, 785.

[69] Becke, A. D. (1988) Density-functional exchange-energy approximation with correct asymptotic behavior, Physical review A 38, 3098.

[70] Stephens, P., Devlin, F., Chabalowski, C., and Frisch, M. J. (1994) Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields, The Journal of Physical Chemistry 98, 11623-11627.

[71] Hehre, W. J., Ditchfield, R., and Pople, J. A. (1972) Self—consistent molecular orbital methods.

XII. Further extensions of gaussian—type basis sets for use in molecular orbital studies of organic molecules, The Journal of Chemical Physics 56, 2257-2261.

[72] Thiel, W. (2014) Semiempirical quantum–chemical methods, Wiley Interdisciplinary Reviews:

Computational Molecular Science 4, 145-157.

[73] Alekseev, N., Luchinin, V., and Charykov, N. (2013) Simulating the conditions for the formation of graphene and graphene nanowalls by semiempirical quantum chemical methods, Russian Journal of Physical Chemistry A 87, 1721-1730.

[74] Kreja, I. (2011) A literature review on computational models for laminated composite and sandwich panels, Open Engineering 1, 59-80.

(32)

15

[75] Lipinski, C. A., Lombardo, F., Dominy, B. W., and Feeney, P. J. (2012) Experimental and computational approaches to estimate solubility and permeability in drug discovery and development settings, Advanced drug delivery reviews 64, 4-17.

[76] Cramer, C. J. (2013) Essentials of computational chemistry: theories and models, John Wiley &

Sons.

[77] Sadlej, J., Dobrowolski, J. C., and Rode, J. E. (2010) VCD spectroscopy as a novel probe for chirality transfer in molecular interactions, Chemical Society Reviews 39, 1478-1488.

[78] Rega, N., Cossi, M., and Barone, V. (1999) Improving performance of polarizable continuum model for study of large molecules in solution, Journal of computational chemistry 20, 1186-1198.

[79] Marenich, A. V., Cramer, C. J., and Truhlar, D. G. (2009) Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions, The Journal of Physical Chemistry B 113, 6378-6396.

[80] Dennington, R., Keith, T., and Millam, J. (2009) Semichem Inc, Shawnee Mission KS, GaussView, Version 5.

[81] Frisch, M., Trucks, G., Schlegel, H., Scuseria, G., Robb, M., Cheeseman, J., Scalmani, G., Barone, V., Mennucci, B., and Petersson, G. (2009) gaussian 09, Gaussian, Inc., Wallingford, CT 4.

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CHAPTER 2 DFT Study of the Interactions between DOTA Chelator and Competitive Alkali Metal Ions

E. Frimpong, A. A. Skelton^*, B. Honarparvar^*

School of Pharmacy and Pharmacology, University of KwaZulu-Natal, Durban 4001, South Africa Corresponding authors: [email protected] (B. Honarparvar), [email protected] (A.A Skelton) School of Pharmacy and Pharmacology, University of KwaZulu-Natal, Durban 4001, South Africa. Tel.: +27 31 26084, +27 31 2608520

Abstract

1, 4, 7, 10-tetraazacyclododecane-1, 4, 7, 10-tetracetic acid (DOTA) is an important chelator for radiolabeling of pharmaceuticals. The ability of alkali metals, found in the body, to complex with DOTA and compete with radio metals can alter the radiolabeling process. Non-covalent interactions between DOTA complexed with alkali metals, Li⁺, Na⁺, K⁺ and Rb⁺, were investigated with density functional theory using B3LYP and ωB97XD functionals with 6-311+G (2d, 2p) basis set for Li⁺, Na⁺ and K⁺ and Def2-TZVPD for Rb⁺. Conformational possibilities were explored in terms of a different number of carboxylic pendant arms of DOTA in in close proximity to the ions. It is found that the case in which four arms of DOTA are interacting with ions is more stable in comparison to other conformations.

The core objective of this study is to explore the electronic structure properties upon complexation of alkali metals, Li⁺ Na⁺, K⁺ and Rb⁺, with DOTA chelator. Interaction energies, relaxation energies, entropies, Gibbs free energies and enthalpies show that the stability of DOTA, complexed with alkali metals decreases down the group of the periodic table. Implicit water solvation affects the complexation of DOTA―ions leading to decreases in the stability of the complexes. NBO analysis through the natural population charges and the second order perturbation theory reveals charge transfer between DOTA and alkali metals. Conceptual DFT-based properties such as HOMO/LUMO energies, ΔEHOMO-LUMO and chemical hardness and softness reveal the decrease in chemical stability of

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DOTA―alkali metal complexes down the alkali metal series. This study serves as a guide to researchers in the field of organometallic chelators, particularly, radio-pharmaceuticals in finding the efficient optimal match between chelators and different metal ions.

Keywords: Density functional theory (DFT); 1, 4, 7, 10-tetraazacyclododecane-1, 4, 7, 10-tetracetic acid (DOTA); Natural bond orbital (NBO).

2.1 Introduction

Organometallic chelators can be potentially used for radio-metal-based pharmaceuticals ^{1, 2} where the radiolabeled chelator complexes are used as biological vehicles for imaging in the field of medicine^3,

4. The bifunctional chelator, which is covalently bound to a lead compound forms a stable chelator―ion complex to deliver an isotope, as a labelling agent, towards a specific in vivo target ⁵. The 1, 4, 7, 10-tetra acetic acid, DOTA, is a twelve-membered tetra aza macro cycle (Figure 1), which contains four pendant carboxylate arms connected to cyclen amines.

Figure 1. The structure of 1, 4, 7, 10-tetraazacyclododecane-1, 4, 7, 10-tetraacetic acid (DOTA)

Several pharmacokinetic and structural studies in the field of coordination chemistry have been performed on radio metals complexes, with DOTA derivatives, to gain deep insight into metal based pharmaceutics ^6-11 . To the best of our knowledge, despite comprehensive efforts made on radio-metals complexed with DOTA chelator, there has been less attention on finding the optimal match of DOTA chelator with alkali metal ions, found in the body, which can act as competitors to radio metals. In the light of this fact, the present study reports electronic structure calculations using density functional theory (B3LYP functional) with 6-311+G (2d, 2p) basis set for Li⁺, Na⁺and K⁺ and Def2-TZVPD for Rb⁺ to provide insight into the essential factors affecting the chelating ability of DOTA with alkali

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metals. This can be expanded into exploiting the possible impacts of these competitive ions on the radiolabeling yield of this chelator, which is useful in predicting the efficiency of the complexation of DOTA with radio metals, in the presence of other ions, in vivo. To gain an in-depth insight into the complexation of DOTA with alkali metals, the interaction of DOTA―alkali metal complexes and other thermodynamic properties such as relaxation energies, entropy, enthalpy, Gibbs free energy, and the interatomic distances within DOTA-alkali metal complexes will be reported. NBO analysis and DFT- based reactivity descriptors, the electron affinity (EA), ionization potential (IP), chemical softness (S) and hardness (η) are also discussed.

2.2 Computational details

The B3LYP density functional is widely used for in silico electronic structure analysis because it could give reasonable energies, molecular structures and vibrational frequencies ^{12, 13}. B3LYP density functional ^14-16 with 6-311G+ (2d, 2p) basis set using Gaussian 09 program¹⁷ were employed in the present study for DOTA chelator and the selected Li⁺, Na⁺and K⁺ions. The Def2-TPVZ basis set was used for Rb⁺, which is described by the effective core potential (ECP) of Wadt and Hay ^18-23. Full geometry optimizations of all the species were carried out. BSSE calculations are performed to test the effect of a finite basis set. Interaction energy (Eint) is defined as:

𝐸_int = 𝐸DOTA−ion complex− 𝐸_DOTA− 𝐸_ion (𝟏)

The ion described in the equation could be Li⁺, Na⁺, K⁺ and Rb⁺Relaxation energies were calculated by subtracting the complexation energy values (unrelaxed) from the interaction energies (relaxed).

After the geometry optimization of the DOTA―cation complexes, the cation was removed from DOTA and a single point energy of DOTA in the same configuration was performed. Secondly, a further geometry optimization of the DOTA was performed to enable DOTA to relax. The differences in energies between the two aforementioned cases is called the relaxation energy, which provides a measure of how the ion affects the conformation of the DOTA. Intermolecular short-range distances

≤3.5Å between the ions and the hetero atoms are recorded. To consider the long-range and dispersion contribution in the Eint values of DOTA―ion further calculations were performed with the ωB97XD density functional.²⁴

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Natural bond orbital (NBO) analysis was performed using NBO program implemented in Gaussian 09 program package. NBO analysis could highlight the role of intermolecular orbital interaction in the complexes, particularly the charge transfer between DOTA and ions by considering all possible interactions between filled donor and empty acceptor NBOs, and estimating their energetic significance with second-order perturbation theory. The second-order Fock matrix was employed to evaluate the donor-acceptor interactions in the NBO basis²⁵. Second perturbation theory confirms whether there is an electron donation from one atom to another. This electron donation results in the stabilization of energy, 𝐸²:

𝐸² =^𝑞^𝑖^{𝐹(𝑖,𝑗)}²

𝜀_𝑗−𝜀_𝑖 (2)

Here qi is the orbital occupancy, while εi, εj and Fi, j are the diagonal and the off-diagonal NBO Fock matrix elements, respectively.

Atoms in each complex were categorized in terms of their short-range distance with ions (≤3.5Å range), after the geometry optimizations. The DFT based reactivity descriptors calculations were preformed using the following equations ^26-29:

Chemical hardness is defined as:

η =𝐼𝑃 − 𝐸𝐴

2 (𝟑) and softness,

S = 1

2𝜂 (𝟒)

Ionization potential (IP) was obtained by using energy differences, between radical cation, Ec and the respective neutral molecule, 𝐼𝑃 = 𝐸_𝑐 − 𝐸_𝑛. Electron affinity (EA) was calculated by the energy differences between a radical anion, Ea and the respective neutral molecule, 𝐸𝐴 = 𝐸_𝑎− 𝐸_𝑛. The term

“neutral” is the standard charge state, for instance, the ions have +1 charge and cationic and anionic species have +2 and 0 charges, respectively. Thermodynamic properties (enthalpy, free energy and entropy with different translational, vibrational and rotational contributions) are calculated by normal mode analysis ³⁰ The Polarizable Continuum Model (PCM), using the integral equation-formalism polarizable continuum model (IEF-PCM), was used to evaluate the solvent effect on the NOTA complexation with alkali metals³¹ ³¹ Finally, the eigenvalues of the highest occupied molecular orbital